How Does Weight Affect Speed of a Soap Box Car?

[Haleybell514]

Homework Statement

I was wondering about how the placement of weight affects Soap Box Cars. I have been racing them for 5 years now, and I cannot find any information. I was wondering if there was a formula to find the relationship between speed and weight, and how to solve it. For instance, if the car runs faster because weight is in the back, what is the reason for this? Why not the front?

Homework Equations

I found the equation:
a= g sin (θ) - kv2/m
Being in middle school, I am not sure what it means. Please help!

The Attempt at a Solution

 

[scientific601]

Overall weight or weight distribution about its center of mass shouldn't matter directly. However, if there is non symmetrical friction between front vs. back wheels on the ground (wether poor bearings, rubber deflection), then these may vary with the weight applied at their specific locations. For example, if you have premium bearings and hard rubber on the back wheels it makes sense to place more weight there because those wheels will be able to handle more without penalty. The worse performing wheels will still drag the speed down somewhat even if they just roll along.

The formula looks to be an acceleration relationship depending on the slope angle (hill). That's not influenced by weight, ideally. Friction and air resistance are your main concerns.

 

[Haleybell514]

If we assume that the only variable between two cars is weight placement, because we do a wheel swap and a lane change, is there a better formula to use instead of the one I found? If there is a more simple formula, could you explain it to me?

 

[rcgldr]

Since the ramp levels out, there is a small advantage to having the center of mass as far back as possible, which translates into having the center of mass a bit higher at the start, but ending up at about the same height as a forwards center of mass when the ramp levels out. The result is a greater change in gravitational potential energy.

A heavier cart may experience relatively higher rolling resistance and friction, but relatively lower aerodynamic drag. I suspect the drag isn't as much of a factor as rolling resistance and friction, so lighter may be better, or perhaps there's some ideal weight range.